High-order harmonics can be efficiently generated by high power mid-infrared ultrashort laser excitation of semiconductor materials. Interaction of an intense femtosecond pulse with finite structures involves a complex interplay of linear and nonlinear propagation effects and electron-hole carrier dynamics, which can be self-consistently analyzed numerically by a coupled Maxwell-Semiconductor Bloch model. In the current work, such an approach based on a three-band model for gallium arsenide  is applied to elucidate the influence of multiple reflections and transmissions from a finite slab on the high-order harmonic emission. Reflected and transmitted spectra including even and odd harmonics are theoretically analyzed as a function of the slab thickness and the field amplitude. Spatial distributions of laser-induced carriers are shown to be strongly inhomogeneous and thickness-dependent. The developed approach opens new frontiers for exploring ultrashort laser interaction regimes with nanostructures of arbitrary geometry.